An electric power network includes buses connected to transmission lines. The buses are connected to generators and loads. Optimal power flow (OPF) analysis is often used for monitoring and controlling the operation of the network. The power flow depends, in part, on voltage magnitudes and phase angles. Generation amounts and voltage levels on the buses are optimized by minimizing an objective function subject to constraints, such as the magnitudes, phases, power transferred, generator capacity, thermal losses, and the like.
Most conventional OFF optimizations:                1) Use simplifying assumptions, such as small differences between phase angles at buses, to reduce quadratic equalities and inequalities to linear equalities and inequalities. However, such assumptions may not be valid for all networks.        2) Use nonlinear programming (NLP) to determine a lowest cost per kilowatt hour delivered. However, NLP cannot guarantee the globally optimal voltages and generator levels for efficient operation.        3) Use a relaxation of OPF to convex optimization, such as second-order cone programming (SOCP). However, such relaxed convex optimizations do not guarantee feasible solutions with a global minimum for the original problem.        4) Use a relaxation of OPF to semi-definite programming (SDP), which requires changing resistances of lossless lines in the network, restrictions on the network topology or constraints, or require modification of the network to ensure global optimality.        5) Use a branch & bound (BB) procedure with Lagrangian duality (LD) based lower bounds that do not consider all necessary constraints and are considerably slow due to the irregular nature of the optimization problem.        
Thus, there remains a need to globally optimize an electric power networks in an efficient and expedient manner.
U.S. Pat. No. 6,625,520 describes a system and method for operating an electric power system that calculates optimal power flow and available transfer capability of the electric power system based on the optimal power flow. The system derives data associated with the initial phase angle and maximum electric power value of a generator by calculating mechanical output and electrical output of a generator, including a generator phase angle defined by a time function in a condition that the generator phase angle does not exceed a preset value.